Question:

A photo-cell is illuminated by a source of light,which is placed at a distance d from the cell.If the distance become d/2, then number of electrons emited per second will be

Updated On: Apr 21, 2025

Remain same
Four times
Two times
One-fourth

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The Correct Option is B

Solution and Explanation

The correct option is(B): Four times The intensity (I) of light is given by the formula: I = E / (At) Here, E represents the total energy of the light source, A is the area of the illuminated surface, and t is the time.Thus, we can express I as: I = (4πr^2 tE) / (4πr^2) Now, consider the ratio of two intensities, I2/I1: (I2/I1) = [(4πr2 tE) / (4πr1^2 tE)] Simplifying this expression: (I2/I1) = (r1^2 / r2^2) This ratio shows that I2/I1 is equal to 1/4. This relationship indicates that the number of photoelectrons emitted is directly proportional to the intensity of light. Therefore, the number of electrons emitted one-quarter of the initial number.

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Concepts Used:

Photoelectric Effect

When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.

Photoelectric Effect Formula:

According to Einstein’s explanation of the photoelectric effect :

The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron

i.e. hν = W + E

Where,

h is Planck’s constant.
ν is the frequency of the incident photon.
W is a work function.
E is the maximum kinetic energy of ejected electrons: 1/2 mv².

Laws of Photoelectric Effect:

The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
The process of photo-emission is an instantaneous process.